1. Field of the Invention
The present invention relates to a phase shift angle detector for detecting the phase shift angle of a carrier wave, used in a demodulator, of a multiphase modulated signal, such as 4-phase or 8-phase modulated signal. Such a system may be utilized voice frequency cable communication, such as with a telephone.
2. Description of the Prior Art
A typical phase shift angle detector is shown in FIG. 2. The phase shift angle detector receives a multiphase modulated signal .delta.(t) EQU .delta.(t)=A cos (.omega.ct+g(t)+.phi.e) (1
in which A is an amplitude, .omega.c is an angular frequency, .phi.e is a phase shift, and g(t) is the modulated signal. The multiphase modulated signal .delta.(t) is applied to multipliers 21 and 22. In multiplier 21, the signal .delta.(t) is multiplied by the signal cos .omega.ct having the same phase component as that of the input signal .delta.(t). Further in in multiplier 22, the signal .delta.(t) is multiplied by the signal sin .omega.ct having a phase which is phase shifted 90 degrees from the phase of the input signal .delta.(t). Thus, multipliers 21 and 22 generate signals which can be expressed, respectively, by the following equations (2) and (3). EQU 1/2A{ cos (2.omega.ct+.phi.e+g(t))+cos (.phi.e+g(t))} (2) EQU 1/2A{ sin (2.omega.ct+.phi.e+g(t))+sin (.phi.e+g(t))} (3)
The output signals (2) and (3) from multipliers 21 and 22 are applied to low pass filters 23 and 24, respectively, for deleting the signals having an angular frequency 2.omega.ct. Thus, low pass filters 23 and 24 generate signals which can be expressed by the following equations (4) and (5), respectively. EQU 1/2A cos (.phi.e+g(t)) (4) EQU 1/2A sin (.phi.e+g(t)) (5)
Then, signals (4) and (5) are applied to a decision device 25 so that signals (4) and (5) are changed to signals given by the following equations (6) and (7), respectively. EQU 1/2A cos (g(t)) (6) EQU 1/2A sin (g(t)) (7)
The signals (6) and (7) produced from the decision device 25 are applied together with the signals (4) and (5) from the low pass filters to multipliers 26, 27, 28 and 29 and further to adders 30 and 31 in a manner shown in FIG. 2. This is so that adders 30 and 31 generate signals which can be expressed by the following equations (8) and (9), respectively. EQU 1/2A.sup.2 cos .phi.e (8) EQU 1/2A.sup.2 sin .phi.e (9)
From these two signals (8) and (9), inverse tangent (tan.sup.-1) is calculated in calculator 32 to obtain phase shift angle .phi.e.
The above can be further explained as follows.
.When the multiphase modulated signal .delta.(t) is expressed as, EQU .delta.(t)=e.sup.j {.omega.ct+g(t)+.phi.e} (10)
the amplitude of the carrier metered in the same phase component and the orthogonal phase component can be expressed on the rectangular coordinate axis by the following equation (11), EQU Z(t)=e.sup.j {g(t)+.phi.e} (11)
When the output of the decision device 25 is expressed as, EQU D(t)=e.sup.j {g(t)} (12)
the phase shift angel can be given by the following equation (13). EQU .phi.e=tan.sup.-1 [Z(t).multidot.conj{D(t)}] (13)
("conj" represents a conjugate complex number)
According to the prior art phase shift angle detector, since the decision device 25 is necessary, the circuit is complicated.